Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,10,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(91.1613430010\) |
Analytic rank: | \(1\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.21 | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 39.7755 | 1.75784 | 0.878922 | − | 0.476965i | \(-0.158263\pi\) | ||||
0.878922 | + | 0.476965i | \(0.158263\pi\) | |||||||
\(3\) | 81.0000 | 0.577350 | ||||||||
\(4\) | 1070.09 | 2.09002 | ||||||||
\(5\) | −1731.07 | −1.23866 | −0.619328 | − | 0.785132i | \(-0.712595\pi\) | ||||
−0.619328 | + | 0.785132i | \(0.712595\pi\) | |||||||
\(6\) | 3221.81 | 1.01489 | ||||||||
\(7\) | −3884.78 | −0.611541 | −0.305771 | − | 0.952105i | \(-0.598914\pi\) | ||||
−0.305771 | + | 0.952105i | \(0.598914\pi\) | |||||||
\(8\) | 22198.2 | 1.91608 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | −68854.3 | −2.17736 | ||||||||
\(11\) | 56874.0 | 1.17124 | 0.585621 | − | 0.810585i | \(-0.300851\pi\) | ||||
0.585621 | + | 0.810585i | \(0.300851\pi\) | |||||||
\(12\) | 86677.2 | 1.20667 | ||||||||
\(13\) | −109727. | −1.06554 | −0.532770 | − | 0.846260i | \(-0.678849\pi\) | ||||
−0.532770 | + | 0.846260i | \(0.678849\pi\) | |||||||
\(14\) | −154519. | −1.07499 | ||||||||
\(15\) | −140217. | −0.715138 | ||||||||
\(16\) | 335060. | 1.27815 | ||||||||
\(17\) | −653147. | −1.89667 | −0.948333 | − | 0.317276i | \(-0.897232\pi\) | ||||
−0.948333 | + | 0.317276i | \(0.897232\pi\) | |||||||
\(18\) | 260967. | 0.585948 | ||||||||
\(19\) | −175919. | −0.309686 | −0.154843 | − | 0.987939i | \(-0.549487\pi\) | ||||
−0.154843 | + | 0.987939i | \(0.549487\pi\) | |||||||
\(20\) | −1.85240e6 | −2.58881 | ||||||||
\(21\) | −314668. | −0.353074 | ||||||||
\(22\) | 2.26219e6 | 2.05886 | ||||||||
\(23\) | −1.42571e6 | −1.06233 | −0.531163 | − | 0.847270i | \(-0.678245\pi\) | ||||
−0.531163 | + | 0.847270i | \(0.678245\pi\) | |||||||
\(24\) | 1.79806e6 | 1.10625 | ||||||||
\(25\) | 1.04349e6 | 0.534269 | ||||||||
\(26\) | −4.36446e6 | −1.87305 | ||||||||
\(27\) | 531441. | 0.192450 | ||||||||
\(28\) | −4.15706e6 | −1.27813 | ||||||||
\(29\) | 7.18211e6 | 1.88565 | 0.942825 | − | 0.333288i | \(-0.108158\pi\) | ||||
0.942825 | + | 0.333288i | \(0.108158\pi\) | |||||||
\(30\) | −5.57720e6 | −1.25710 | ||||||||
\(31\) | −6.64880e6 | −1.29305 | −0.646526 | − | 0.762892i | \(-0.723779\pi\) | ||||
−0.646526 | + | 0.762892i | \(0.723779\pi\) | |||||||
\(32\) | 1.96168e6 | 0.330714 | ||||||||
\(33\) | 4.60680e6 | 0.676217 | ||||||||
\(34\) | −2.59792e7 | −3.33404 | ||||||||
\(35\) | 6.72485e6 | 0.757489 | ||||||||
\(36\) | 7.02085e6 | 0.696672 | ||||||||
\(37\) | 8.37955e6 | 0.735043 | 0.367522 | − | 0.930015i | \(-0.380206\pi\) | ||||
0.367522 | + | 0.930015i | \(0.380206\pi\) | |||||||
\(38\) | −6.99726e6 | −0.544380 | ||||||||
\(39\) | −8.88792e6 | −0.615190 | ||||||||
\(40\) | −3.84268e7 | −2.37336 | ||||||||
\(41\) | 1.93751e7 | 1.07082 | 0.535410 | − | 0.844592i | \(-0.320157\pi\) | ||||
0.535410 | + | 0.844592i | \(0.320157\pi\) | |||||||
\(42\) | −1.25161e7 | −0.620648 | ||||||||
\(43\) | −2.28822e7 | −1.02068 | −0.510339 | − | 0.859973i | \(-0.670480\pi\) | ||||
−0.510339 | + | 0.859973i | \(0.670480\pi\) | |||||||
\(44\) | 6.08602e7 | 2.44792 | ||||||||
\(45\) | −1.13576e7 | −0.412885 | ||||||||
\(46\) | −5.67085e7 | −1.86740 | ||||||||
\(47\) | −5.30532e7 | −1.58588 | −0.792942 | − | 0.609297i | \(-0.791452\pi\) | ||||
−0.792942 | + | 0.609297i | \(0.791452\pi\) | |||||||
\(48\) | 2.71399e7 | 0.737942 | ||||||||
\(49\) | −2.52621e7 | −0.626017 | ||||||||
\(50\) | 4.15054e7 | 0.939161 | ||||||||
\(51\) | −5.29049e7 | −1.09504 | ||||||||
\(52\) | −1.17418e8 | −2.22700 | ||||||||
\(53\) | −5.99352e7 | −1.04338 | −0.521688 | − | 0.853136i | \(-0.674698\pi\) | ||||
−0.521688 | + | 0.853136i | \(0.674698\pi\) | |||||||
\(54\) | 2.11383e7 | 0.338297 | ||||||||
\(55\) | −9.84532e7 | −1.45077 | ||||||||
\(56\) | −8.62354e7 | −1.17176 | ||||||||
\(57\) | −1.42494e7 | −0.178797 | ||||||||
\(58\) | 2.85672e8 | 3.31468 | ||||||||
\(59\) | 1.21174e7 | 0.130189 | ||||||||
\(60\) | −1.50045e8 | −1.49465 | ||||||||
\(61\) | 1.37319e8 | 1.26983 | 0.634916 | − | 0.772581i | \(-0.281035\pi\) | ||||
0.634916 | + | 0.772581i | \(0.281035\pi\) | |||||||
\(62\) | −2.64459e8 | −2.27298 | ||||||||
\(63\) | −2.54881e7 | −0.203847 | ||||||||
\(64\) | −9.35241e7 | −0.696809 | ||||||||
\(65\) | 1.89946e8 | 1.31984 | ||||||||
\(66\) | 1.83238e8 | 1.18868 | ||||||||
\(67\) | −2.40791e8 | −1.45983 | −0.729917 | − | 0.683536i | \(-0.760441\pi\) | ||||
−0.729917 | + | 0.683536i | \(0.760441\pi\) | |||||||
\(68\) | −6.98925e8 | −3.96406 | ||||||||
\(69\) | −1.15483e8 | −0.613334 | ||||||||
\(70\) | 2.67484e8 | 1.33155 | ||||||||
\(71\) | 2.40527e8 | 1.12332 | 0.561658 | − | 0.827369i | \(-0.310164\pi\) | ||||
0.561658 | + | 0.827369i | \(0.310164\pi\) | |||||||
\(72\) | 1.45643e8 | 0.638693 | ||||||||
\(73\) | 1.45532e8 | 0.599798 | 0.299899 | − | 0.953971i | \(-0.403047\pi\) | ||||
0.299899 | + | 0.953971i | \(0.403047\pi\) | |||||||
\(74\) | 3.33301e8 | 1.29209 | ||||||||
\(75\) | 8.45230e7 | 0.308460 | ||||||||
\(76\) | −1.88249e8 | −0.647249 | ||||||||
\(77\) | −2.20943e8 | −0.716263 | ||||||||
\(78\) | −3.53521e8 | −1.08141 | ||||||||
\(79\) | −4.07178e8 | −1.17615 | −0.588075 | − | 0.808806i | \(-0.700114\pi\) | ||||
−0.588075 | + | 0.808806i | \(0.700114\pi\) | |||||||
\(80\) | −5.80014e8 | −1.58319 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | 7.70653e8 | 1.88233 | ||||||||
\(83\) | 3.98650e8 | 0.922019 | 0.461009 | − | 0.887395i | \(-0.347487\pi\) | ||||
0.461009 | + | 0.887395i | \(0.347487\pi\) | |||||||
\(84\) | −3.36722e8 | −0.737929 | ||||||||
\(85\) | 1.13065e9 | 2.34932 | ||||||||
\(86\) | −9.10149e8 | −1.79419 | ||||||||
\(87\) | 5.81751e8 | 1.08868 | ||||||||
\(88\) | 1.26250e9 | 2.24419 | ||||||||
\(89\) | −2.64491e6 | −0.00446844 | −0.00223422 | − | 0.999998i | \(-0.500711\pi\) | ||||
−0.00223422 | + | 0.999998i | \(0.500711\pi\) | |||||||
\(90\) | −4.51753e8 | −0.725788 | ||||||||
\(91\) | 4.26267e8 | 0.651622 | ||||||||
\(92\) | −1.52564e9 | −2.22028 | ||||||||
\(93\) | −5.38553e8 | −0.746543 | ||||||||
\(94\) | −2.11022e9 | −2.78774 | ||||||||
\(95\) | 3.04529e8 | 0.383594 | ||||||||
\(96\) | 1.58896e8 | 0.190938 | ||||||||
\(97\) | 1.02578e9 | 1.17647 | 0.588237 | − | 0.808689i | \(-0.299822\pi\) | ||||
0.588237 | + | 0.808689i | \(0.299822\pi\) | |||||||
\(98\) | −1.00481e9 | −1.10044 | ||||||||
\(99\) | 3.73151e8 | 0.390414 | ||||||||
\(100\) | 1.11663e9 | 1.11663 | ||||||||
\(101\) | −1.75741e9 | −1.68046 | −0.840228 | − | 0.542233i | \(-0.817579\pi\) | ||||
−0.840228 | + | 0.542233i | \(0.817579\pi\) | |||||||
\(102\) | −2.10432e9 | −1.92491 | ||||||||
\(103\) | −1.93271e9 | −1.69199 | −0.845996 | − | 0.533189i | \(-0.820993\pi\) | ||||
−0.845996 | + | 0.533189i | \(0.820993\pi\) | |||||||
\(104\) | −2.43575e9 | −2.04166 | ||||||||
\(105\) | 5.44713e8 | 0.437337 | ||||||||
\(106\) | −2.38395e9 | −1.83409 | ||||||||
\(107\) | −4.90766e8 | −0.361949 | −0.180975 | − | 0.983488i | \(-0.557925\pi\) | ||||
−0.180975 | + | 0.983488i | \(0.557925\pi\) | |||||||
\(108\) | 5.68689e8 | 0.402224 | ||||||||
\(109\) | 1.67260e9 | 1.13494 | 0.567470 | − | 0.823394i | \(-0.307922\pi\) | ||||
0.567470 | + | 0.823394i | \(0.307922\pi\) | |||||||
\(110\) | −3.91602e9 | −2.55022 | ||||||||
\(111\) | 6.78744e8 | 0.424378 | ||||||||
\(112\) | −1.30164e9 | −0.781643 | ||||||||
\(113\) | −1.07595e9 | −0.620780 | −0.310390 | − | 0.950609i | \(-0.600460\pi\) | ||||
−0.310390 | + | 0.950609i | \(0.600460\pi\) | |||||||
\(114\) | −5.66778e8 | −0.314298 | ||||||||
\(115\) | 2.46802e9 | 1.31586 | ||||||||
\(116\) | 7.68549e9 | 3.94104 | ||||||||
\(117\) | −7.19921e8 | −0.355180 | ||||||||
\(118\) | 4.81974e8 | 0.228852 | ||||||||
\(119\) | 2.53734e9 | 1.15989 | ||||||||
\(120\) | −3.11257e9 | −1.37026 | ||||||||
\(121\) | 8.76708e8 | 0.371810 | ||||||||
\(122\) | 5.46193e9 | 2.23217 | ||||||||
\(123\) | 1.56938e9 | 0.618238 | ||||||||
\(124\) | −7.11480e9 | −2.70250 | ||||||||
\(125\) | 1.57464e9 | 0.576881 | ||||||||
\(126\) | −1.01380e9 | −0.358331 | ||||||||
\(127\) | 4.53115e9 | 1.54558 | 0.772790 | − | 0.634661i | \(-0.218860\pi\) | ||||
0.772790 | + | 0.634661i | \(0.218860\pi\) | |||||||
\(128\) | −4.72434e9 | −1.55560 | ||||||||
\(129\) | −1.85346e9 | −0.589289 | ||||||||
\(130\) | 7.55520e9 | 2.32007 | ||||||||
\(131\) | 1.76844e9 | 0.524651 | 0.262325 | − | 0.964979i | \(-0.415511\pi\) | ||||
0.262325 | + | 0.964979i | \(0.415511\pi\) | |||||||
\(132\) | 4.92968e9 | 1.41331 | ||||||||
\(133\) | 6.83407e8 | 0.189386 | ||||||||
\(134\) | −9.57757e9 | −2.56616 | ||||||||
\(135\) | −9.19964e8 | −0.238379 | ||||||||
\(136\) | −1.44987e10 | −3.63416 | ||||||||
\(137\) | 5.62271e9 | 1.36365 | 0.681825 | − | 0.731515i | \(-0.261186\pi\) | ||||
0.681825 | + | 0.731515i | \(0.261186\pi\) | |||||||
\(138\) | −4.59339e9 | −1.07815 | ||||||||
\(139\) | 2.41920e9 | 0.549673 | 0.274837 | − | 0.961491i | \(-0.411376\pi\) | ||||
0.274837 | + | 0.961491i | \(0.411376\pi\) | |||||||
\(140\) | 7.19619e9 | 1.58317 | ||||||||
\(141\) | −4.29731e9 | −0.915610 | ||||||||
\(142\) | 9.56709e9 | 1.97462 | ||||||||
\(143\) | −6.24064e9 | −1.24801 | ||||||||
\(144\) | 2.19833e9 | 0.426051 | ||||||||
\(145\) | −1.24328e10 | −2.33567 | ||||||||
\(146\) | 5.78859e9 | 1.05435 | ||||||||
\(147\) | −2.04623e9 | −0.361431 | ||||||||
\(148\) | 8.96686e9 | 1.53625 | ||||||||
\(149\) | 3.82633e9 | 0.635981 | 0.317991 | − | 0.948094i | \(-0.396992\pi\) | ||||
0.317991 | + | 0.948094i | \(0.396992\pi\) | |||||||
\(150\) | 3.36194e9 | 0.542225 | ||||||||
\(151\) | 1.04501e10 | 1.63577 | 0.817885 | − | 0.575382i | \(-0.195147\pi\) | ||||
0.817885 | + | 0.575382i | \(0.195147\pi\) | |||||||
\(152\) | −3.90509e9 | −0.593383 | ||||||||
\(153\) | −4.28530e9 | −0.632222 | ||||||||
\(154\) | −8.78813e9 | −1.25908 | ||||||||
\(155\) | 1.15096e10 | 1.60165 | ||||||||
\(156\) | −9.51086e9 | −1.28576 | ||||||||
\(157\) | −9.41439e9 | −1.23664 | −0.618321 | − | 0.785926i | \(-0.712187\pi\) | ||||
−0.618321 | + | 0.785926i | \(0.712187\pi\) | |||||||
\(158\) | −1.61957e10 | −2.06749 | ||||||||
\(159\) | −4.85475e9 | −0.602393 | ||||||||
\(160\) | −3.39581e9 | −0.409641 | ||||||||
\(161\) | 5.53860e9 | 0.649656 | ||||||||
\(162\) | 1.71220e9 | 0.195316 | ||||||||
\(163\) | 7.04946e9 | 0.782189 | 0.391094 | − | 0.920351i | \(-0.372097\pi\) | ||||
0.391094 | + | 0.920351i | \(0.372097\pi\) | |||||||
\(164\) | 2.07331e10 | 2.23803 | ||||||||
\(165\) | −7.97471e9 | −0.837601 | ||||||||
\(166\) | 1.58565e10 | 1.62077 | ||||||||
\(167\) | −2.24805e9 | −0.223657 | −0.111828 | − | 0.993728i | \(-0.535671\pi\) | ||||
−0.111828 | + | 0.993728i | \(0.535671\pi\) | |||||||
\(168\) | −6.98506e9 | −0.676517 | ||||||||
\(169\) | 1.43560e9 | 0.135377 | ||||||||
\(170\) | 4.49720e10 | 4.12973 | ||||||||
\(171\) | −1.15420e9 | −0.103229 | ||||||||
\(172\) | −2.44859e10 | −2.13324 | ||||||||
\(173\) | −1.65130e9 | −0.140159 | −0.0700793 | − | 0.997541i | \(-0.522325\pi\) | ||||
−0.0700793 | + | 0.997541i | \(0.522325\pi\) | |||||||
\(174\) | 2.31394e10 | 1.91373 | ||||||||
\(175\) | −4.05375e9 | −0.326727 | ||||||||
\(176\) | 1.90562e10 | 1.49703 | ||||||||
\(177\) | 9.81506e8 | 0.0751646 | ||||||||
\(178\) | −1.05202e8 | −0.00785481 | ||||||||
\(179\) | 3.11437e9 | 0.226742 | 0.113371 | − | 0.993553i | \(-0.463835\pi\) | ||||
0.113371 | + | 0.993553i | \(0.463835\pi\) | |||||||
\(180\) | −1.21536e10 | −0.862937 | ||||||||
\(181\) | −1.29740e10 | −0.898508 | −0.449254 | − | 0.893404i | \(-0.648310\pi\) | ||||
−0.449254 | + | 0.893404i | \(0.648310\pi\) | |||||||
\(182\) | 1.69550e10 | 1.14545 | ||||||||
\(183\) | 1.11228e10 | 0.733138 | ||||||||
\(184\) | −3.16484e10 | −2.03550 | ||||||||
\(185\) | −1.45056e10 | −0.910466 | ||||||||
\(186\) | −2.14212e10 | −1.31231 | ||||||||
\(187\) | −3.71471e10 | −2.22146 | ||||||||
\(188\) | −5.67716e10 | −3.31452 | ||||||||
\(189\) | −2.06453e9 | −0.117691 | ||||||||
\(190\) | 1.21128e10 | 0.674299 | ||||||||
\(191\) | 1.37305e10 | 0.746509 | 0.373255 | − | 0.927729i | \(-0.378242\pi\) | ||||
0.373255 | + | 0.927729i | \(0.378242\pi\) | |||||||
\(192\) | −7.57545e9 | −0.402303 | ||||||||
\(193\) | 3.59947e10 | 1.86737 | 0.933685 | − | 0.358095i | \(-0.116574\pi\) | ||||
0.933685 | + | 0.358095i | \(0.116574\pi\) | |||||||
\(194\) | 4.08010e10 | 2.06806 | ||||||||
\(195\) | 1.53856e10 | 0.762009 | ||||||||
\(196\) | −2.70326e10 | −1.30839 | ||||||||
\(197\) | −3.11152e10 | −1.47189 | −0.735944 | − | 0.677042i | \(-0.763262\pi\) | ||||
−0.735944 | + | 0.677042i | \(0.763262\pi\) | |||||||
\(198\) | 1.48422e10 | 0.686288 | ||||||||
\(199\) | −2.66121e10 | −1.20293 | −0.601466 | − | 0.798898i | \(-0.705416\pi\) | ||||
−0.601466 | + | 0.798898i | \(0.705416\pi\) | |||||||
\(200\) | 2.31637e10 | 1.02370 | ||||||||
\(201\) | −1.95041e10 | −0.842835 | ||||||||
\(202\) | −6.99019e10 | −2.95398 | ||||||||
\(203\) | −2.79010e10 | −1.15315 | ||||||||
\(204\) | −5.66130e10 | −2.28865 | ||||||||
\(205\) | −3.35397e10 | −1.32638 | ||||||||
\(206\) | −7.68743e10 | −2.97426 | ||||||||
\(207\) | −9.35412e9 | −0.354108 | ||||||||
\(208\) | −3.67653e10 | −1.36192 | ||||||||
\(209\) | −1.00052e10 | −0.362717 | ||||||||
\(210\) | 2.16662e10 | 0.768770 | ||||||||
\(211\) | −2.16068e10 | −0.750445 | −0.375223 | − | 0.926935i | \(-0.622434\pi\) | ||||
−0.375223 | + | 0.926935i | \(0.622434\pi\) | |||||||
\(212\) | −6.41360e10 | −2.18067 | ||||||||
\(213\) | 1.94827e10 | 0.648547 | ||||||||
\(214\) | −1.95205e10 | −0.636250 | ||||||||
\(215\) | 3.96107e10 | 1.26427 | ||||||||
\(216\) | 1.17971e10 | 0.368750 | ||||||||
\(217\) | 2.58292e10 | 0.790754 | ||||||||
\(218\) | 6.65284e10 | 1.99505 | ||||||||
\(219\) | 1.17881e10 | 0.346293 | ||||||||
\(220\) | −1.05354e11 | −3.03213 | ||||||||
\(221\) | 7.16682e10 | 2.02098 | ||||||||
\(222\) | 2.69974e10 | 0.745990 | ||||||||
\(223\) | 1.86803e10 | 0.505839 | 0.252919 | − | 0.967487i | \(-0.418609\pi\) | ||||
0.252919 | + | 0.967487i | \(0.418609\pi\) | |||||||
\(224\) | −7.62069e9 | −0.202245 | ||||||||
\(225\) | 6.84636e9 | 0.178090 | ||||||||
\(226\) | −4.27963e10 | −1.09123 | ||||||||
\(227\) | 3.29772e10 | 0.824324 | 0.412162 | − | 0.911111i | \(-0.364774\pi\) | ||||
0.412162 | + | 0.911111i | \(0.364774\pi\) | |||||||
\(228\) | −1.52482e10 | −0.373689 | ||||||||
\(229\) | −8.98402e9 | −0.215879 | −0.107940 | − | 0.994157i | \(-0.534425\pi\) | ||||
−0.107940 | + | 0.994157i | \(0.534425\pi\) | |||||||
\(230\) | 9.81666e10 | 2.31307 | ||||||||
\(231\) | −1.78964e10 | −0.413535 | ||||||||
\(232\) | 1.59430e11 | 3.61306 | ||||||||
\(233\) | −1.36044e10 | −0.302396 | −0.151198 | − | 0.988503i | \(-0.548313\pi\) | ||||
−0.151198 | + | 0.988503i | \(0.548313\pi\) | |||||||
\(234\) | −2.86352e10 | −0.624351 | ||||||||
\(235\) | 9.18391e10 | 1.96436 | ||||||||
\(236\) | 1.29666e10 | 0.272097 | ||||||||
\(237\) | −3.29814e10 | −0.679051 | ||||||||
\(238\) | 1.00924e11 | 2.03891 | ||||||||
\(239\) | 1.11203e10 | 0.220458 | 0.110229 | − | 0.993906i | \(-0.464842\pi\) | ||||
0.110229 | + | 0.993906i | \(0.464842\pi\) | |||||||
\(240\) | −4.69811e10 | −0.914056 | ||||||||
\(241\) | 3.53983e10 | 0.675936 | 0.337968 | − | 0.941158i | \(-0.390260\pi\) | ||||
0.337968 | + | 0.941158i | \(0.390260\pi\) | |||||||
\(242\) | 3.48715e10 | 0.653584 | ||||||||
\(243\) | 3.48678e9 | 0.0641500 | ||||||||
\(244\) | 1.46944e11 | 2.65397 | ||||||||
\(245\) | 4.37305e10 | 0.775420 | ||||||||
\(246\) | 6.24229e10 | 1.08677 | ||||||||
\(247\) | 1.93031e10 | 0.329983 | ||||||||
\(248\) | −1.47592e11 | −2.47759 | ||||||||
\(249\) | 3.22906e10 | 0.532328 | ||||||||
\(250\) | 6.26321e10 | 1.01407 | ||||||||
\(251\) | −1.14639e11 | −1.82305 | −0.911525 | − | 0.411244i | \(-0.865094\pi\) | ||||
−0.911525 | + | 0.411244i | \(0.865094\pi\) | |||||||
\(252\) | −2.72745e10 | −0.426044 | ||||||||
\(253\) | −8.10862e10 | −1.24424 | ||||||||
\(254\) | 1.80229e11 | 2.71689 | ||||||||
\(255\) | 9.15824e10 | 1.35638 | ||||||||
\(256\) | −1.40029e11 | −2.03769 | ||||||||
\(257\) | 5.77628e10 | 0.825942 | 0.412971 | − | 0.910744i | \(-0.364491\pi\) | ||||
0.412971 | + | 0.910744i | \(0.364491\pi\) | |||||||
\(258\) | −7.37221e10 | −1.03588 | ||||||||
\(259\) | −3.25528e10 | −0.449509 | ||||||||
\(260\) | 2.03259e11 | 2.75848 | ||||||||
\(261\) | 4.71218e10 | 0.628550 | ||||||||
\(262\) | 7.03407e10 | 0.922255 | ||||||||
\(263\) | −2.65909e10 | −0.342714 | −0.171357 | − | 0.985209i | \(-0.554815\pi\) | ||||
−0.171357 | + | 0.985209i | \(0.554815\pi\) | |||||||
\(264\) | 1.02263e11 | 1.29569 | ||||||||
\(265\) | 1.03752e11 | 1.29238 | ||||||||
\(266\) | 2.71828e10 | 0.332911 | ||||||||
\(267\) | −2.14238e8 | −0.00257985 | ||||||||
\(268\) | −2.57667e11 | −3.05108 | ||||||||
\(269\) | −3.56944e10 | −0.415638 | −0.207819 | − | 0.978167i | \(-0.566637\pi\) | ||||
−0.207819 | + | 0.978167i | \(0.566637\pi\) | |||||||
\(270\) | −3.65920e10 | −0.419034 | ||||||||
\(271\) | 9.29397e9 | 0.104674 | 0.0523371 | − | 0.998629i | \(-0.483333\pi\) | ||||
0.0523371 | + | 0.998629i | \(0.483333\pi\) | |||||||
\(272\) | −2.18844e11 | −2.42423 | ||||||||
\(273\) | 3.45277e10 | 0.376214 | ||||||||
\(274\) | 2.23646e11 | 2.39709 | ||||||||
\(275\) | 5.93477e10 | 0.625758 | ||||||||
\(276\) | −1.23577e11 | −1.28188 | ||||||||
\(277\) | −5.13710e10 | −0.524275 | −0.262137 | − | 0.965031i | \(-0.584427\pi\) | ||||
−0.262137 | + | 0.965031i | \(0.584427\pi\) | |||||||
\(278\) | 9.62247e10 | 0.966240 | ||||||||
\(279\) | −4.36228e10 | −0.431017 | ||||||||
\(280\) | 1.49280e11 | 1.45141 | ||||||||
\(281\) | −1.45915e10 | −0.139611 | −0.0698057 | − | 0.997561i | \(-0.522238\pi\) | ||||
−0.0698057 | + | 0.997561i | \(0.522238\pi\) | |||||||
\(282\) | −1.70928e11 | −1.60950 | ||||||||
\(283\) | −1.53399e10 | −0.142162 | −0.0710810 | − | 0.997471i | \(-0.522645\pi\) | ||||
−0.0710810 | + | 0.997471i | \(0.522645\pi\) | |||||||
\(284\) | 2.57386e11 | 2.34775 | ||||||||
\(285\) | 2.46668e10 | 0.221468 | ||||||||
\(286\) | −2.48224e11 | −2.19380 | ||||||||
\(287\) | −7.52680e10 | −0.654850 | ||||||||
\(288\) | 1.28706e10 | 0.110238 | ||||||||
\(289\) | 3.08013e11 | 2.59734 | ||||||||
\(290\) | −4.94519e11 | −4.10575 | ||||||||
\(291\) | 8.30884e10 | 0.679238 | ||||||||
\(292\) | 1.55732e11 | 1.25359 | ||||||||
\(293\) | −9.22722e10 | −0.731420 | −0.365710 | − | 0.930729i | \(-0.619174\pi\) | ||||
−0.365710 | + | 0.930729i | \(0.619174\pi\) | |||||||
\(294\) | −8.13896e10 | −0.635340 | ||||||||
\(295\) | −2.09761e10 | −0.161259 | ||||||||
\(296\) | 1.86011e11 | 1.40840 | ||||||||
\(297\) | 3.02252e10 | 0.225406 | ||||||||
\(298\) | 1.52194e11 | 1.11796 | ||||||||
\(299\) | 1.56440e11 | 1.13195 | ||||||||
\(300\) | 9.04470e10 | 0.644687 | ||||||||
\(301\) | 8.88923e10 | 0.624187 | ||||||||
\(302\) | 4.15656e11 | 2.87543 | ||||||||
\(303\) | −1.42350e11 | −0.970212 | ||||||||
\(304\) | −5.89434e10 | −0.395826 | ||||||||
\(305\) | −2.37709e11 | −1.57289 | ||||||||
\(306\) | −1.70450e11 | −1.11135 | ||||||||
\(307\) | −8.99578e10 | −0.577984 | −0.288992 | − | 0.957331i | \(-0.593320\pi\) | ||||
−0.288992 | + | 0.957331i | \(0.593320\pi\) | |||||||
\(308\) | −2.36429e11 | −1.49700 | ||||||||
\(309\) | −1.56549e11 | −0.976872 | ||||||||
\(310\) | 4.57799e11 | 2.81544 | ||||||||
\(311\) | −1.16525e11 | −0.706312 | −0.353156 | − | 0.935564i | \(-0.614891\pi\) | ||||
−0.353156 | + | 0.935564i | \(0.614891\pi\) | |||||||
\(312\) | −1.97296e11 | −1.17875 | ||||||||
\(313\) | 1.26016e11 | 0.742123 | 0.371061 | − | 0.928608i | \(-0.378994\pi\) | ||||
0.371061 | + | 0.928608i | \(0.378994\pi\) | |||||||
\(314\) | −3.74462e11 | −2.17382 | ||||||||
\(315\) | 4.41217e10 | 0.252496 | ||||||||
\(316\) | −4.35717e11 | −2.45817 | ||||||||
\(317\) | 1.70022e11 | 0.945665 | 0.472833 | − | 0.881152i | \(-0.343232\pi\) | ||||
0.472833 | + | 0.881152i | \(0.343232\pi\) | |||||||
\(318\) | −1.93100e11 | −1.05891 | ||||||||
\(319\) | 4.08476e11 | 2.20855 | ||||||||
\(320\) | 1.61897e11 | 0.863107 | ||||||||
\(321\) | −3.97521e10 | −0.208971 | ||||||||
\(322\) | 2.20300e11 | 1.14199 | ||||||||
\(323\) | 1.14901e11 | 0.587371 | ||||||||
\(324\) | 4.60638e10 | 0.232224 | ||||||||
\(325\) | −1.14500e11 | −0.569285 | ||||||||
\(326\) | 2.80396e11 | 1.37497 | ||||||||
\(327\) | 1.35481e11 | 0.655258 | ||||||||
\(328\) | 4.30093e11 | 2.05178 | ||||||||
\(329\) | 2.06100e11 | 0.969833 | ||||||||
\(330\) | −3.17198e11 | −1.47237 | ||||||||
\(331\) | −2.96557e11 | −1.35795 | −0.678973 | − | 0.734163i | \(-0.737575\pi\) | ||||
−0.678973 | + | 0.734163i | \(0.737575\pi\) | |||||||
\(332\) | 4.26590e11 | 1.92703 | ||||||||
\(333\) | 5.49782e10 | 0.245014 | ||||||||
\(334\) | −8.94173e10 | −0.393154 | ||||||||
\(335\) | 4.16827e11 | 1.80823 | ||||||||
\(336\) | −1.05433e11 | −0.451282 | ||||||||
\(337\) | −8.51827e10 | −0.359763 | −0.179882 | − | 0.983688i | \(-0.557571\pi\) | ||||
−0.179882 | + | 0.983688i | \(0.557571\pi\) | |||||||
\(338\) | 5.71018e10 | 0.237971 | ||||||||
\(339\) | −8.71517e10 | −0.358408 | ||||||||
\(340\) | 1.20989e12 | 4.91011 | ||||||||
\(341\) | −3.78144e11 | −1.51448 | ||||||||
\(342\) | −4.59090e10 | −0.181460 | ||||||||
\(343\) | 2.54903e11 | 0.994377 | ||||||||
\(344\) | −5.07944e11 | −1.95570 | ||||||||
\(345\) | 1.99910e11 | 0.759709 | ||||||||
\(346\) | −6.56814e10 | −0.246377 | ||||||||
\(347\) | −2.47414e11 | −0.916098 | −0.458049 | − | 0.888927i | \(-0.651452\pi\) | ||||
−0.458049 | + | 0.888927i | \(0.651452\pi\) | |||||||
\(348\) | 6.22525e11 | 2.27536 | ||||||||
\(349\) | 2.31188e11 | 0.834163 | 0.417081 | − | 0.908869i | \(-0.363053\pi\) | ||||
0.417081 | + | 0.908869i | \(0.363053\pi\) | |||||||
\(350\) | −1.61240e11 | −0.574336 | ||||||||
\(351\) | −5.83136e10 | −0.205063 | ||||||||
\(352\) | 1.11568e11 | 0.387346 | ||||||||
\(353\) | 3.28570e11 | 1.12627 | 0.563134 | − | 0.826366i | \(-0.309596\pi\) | ||||
0.563134 | + | 0.826366i | \(0.309596\pi\) | |||||||
\(354\) | 3.90399e10 | 0.132128 | ||||||||
\(355\) | −4.16371e11 | −1.39140 | ||||||||
\(356\) | −2.83029e9 | −0.00933910 | ||||||||
\(357\) | 2.05524e11 | 0.669663 | ||||||||
\(358\) | 1.23876e11 | 0.398577 | ||||||||
\(359\) | −2.45562e11 | −0.780253 | −0.390126 | − | 0.920761i | \(-0.627569\pi\) | ||||
−0.390126 | + | 0.920761i | \(0.627569\pi\) | |||||||
\(360\) | −2.52118e11 | −0.791121 | ||||||||
\(361\) | −2.91740e11 | −0.904095 | ||||||||
\(362\) | −5.16049e11 | −1.57944 | ||||||||
\(363\) | 7.10133e10 | 0.214664 | ||||||||
\(364\) | 4.56144e11 | 1.36190 | ||||||||
\(365\) | −2.51926e11 | −0.742943 | ||||||||
\(366\) | 4.42416e11 | 1.28874 | ||||||||
\(367\) | −9.21749e10 | −0.265226 | −0.132613 | − | 0.991168i | \(-0.542337\pi\) | ||||
−0.132613 | + | 0.991168i | \(0.542337\pi\) | |||||||
\(368\) | −4.77700e11 | −1.35781 | ||||||||
\(369\) | 1.27120e11 | 0.356940 | ||||||||
\(370\) | −5.76968e11 | −1.60046 | ||||||||
\(371\) | 2.32836e11 | 0.638068 | ||||||||
\(372\) | −5.76299e11 | −1.56029 | ||||||||
\(373\) | −7.33556e11 | −1.96220 | −0.981101 | − | 0.193499i | \(-0.938016\pi\) | ||||
−0.981101 | + | 0.193499i | \(0.938016\pi\) | |||||||
\(374\) | −1.47754e12 | −3.90498 | ||||||||
\(375\) | 1.27546e11 | 0.333062 | ||||||||
\(376\) | −1.17769e12 | −3.03868 | ||||||||
\(377\) | −7.88074e11 | −2.00924 | ||||||||
\(378\) | −8.21178e10 | −0.206883 | ||||||||
\(379\) | 1.43975e11 | 0.358434 | 0.179217 | − | 0.983810i | \(-0.442644\pi\) | ||||
0.179217 | + | 0.983810i | \(0.442644\pi\) | |||||||
\(380\) | 3.25873e11 | 0.801718 | ||||||||
\(381\) | 3.67023e11 | 0.892341 | ||||||||
\(382\) | 5.46136e11 | 1.31225 | ||||||||
\(383\) | −1.57608e11 | −0.374269 | −0.187135 | − | 0.982334i | \(-0.559920\pi\) | ||||
−0.187135 | + | 0.982334i | \(0.559920\pi\) | |||||||
\(384\) | −3.82672e11 | −0.898124 | ||||||||
\(385\) | 3.82469e11 | 0.887204 | ||||||||
\(386\) | 1.43171e12 | 3.28255 | ||||||||
\(387\) | −1.50130e11 | −0.340226 | ||||||||
\(388\) | 1.09768e12 | 2.45885 | ||||||||
\(389\) | 4.23390e11 | 0.937492 | 0.468746 | − | 0.883333i | \(-0.344706\pi\) | ||||
0.468746 | + | 0.883333i | \(0.344706\pi\) | |||||||
\(390\) | 6.11972e11 | 1.33949 | ||||||||
\(391\) | 9.31202e11 | 2.01488 | ||||||||
\(392\) | −5.60773e11 | −1.19950 | ||||||||
\(393\) | 1.43244e11 | 0.302907 | ||||||||
\(394\) | −1.23762e12 | −2.58735 | ||||||||
\(395\) | 7.04856e11 | 1.45685 | ||||||||
\(396\) | 3.99304e11 | 0.815972 | ||||||||
\(397\) | −3.97616e11 | −0.803352 | −0.401676 | − | 0.915782i | \(-0.631572\pi\) | ||||
−0.401676 | + | 0.915782i | \(0.631572\pi\) | |||||||
\(398\) | −1.05851e12 | −2.11457 | ||||||||
\(399\) | 5.53560e10 | 0.109342 | ||||||||
\(400\) | 3.49633e11 | 0.682877 | ||||||||
\(401\) | −3.96502e11 | −0.765766 | −0.382883 | − | 0.923797i | \(-0.625069\pi\) | ||||
−0.382883 | + | 0.923797i | \(0.625069\pi\) | |||||||
\(402\) | −7.75783e11 | −1.48157 | ||||||||
\(403\) | 7.29556e11 | 1.37780 | ||||||||
\(404\) | −1.88059e12 | −3.51218 | ||||||||
\(405\) | −7.45171e10 | −0.137628 | ||||||||
\(406\) | −1.10977e12 | −2.02706 | ||||||||
\(407\) | 4.76579e11 | 0.860914 | ||||||||
\(408\) | −1.17440e12 | −2.09819 | ||||||||
\(409\) | 5.75923e11 | 1.01768 | 0.508838 | − | 0.860862i | \(-0.330075\pi\) | ||||
0.508838 | + | 0.860862i | \(0.330075\pi\) | |||||||
\(410\) | −1.33406e12 | −2.33156 | ||||||||
\(411\) | 4.55439e11 | 0.787304 | ||||||||
\(412\) | −2.06817e12 | −3.53629 | ||||||||
\(413\) | −4.70733e10 | −0.0796159 | ||||||||
\(414\) | −3.72064e11 | −0.622467 | ||||||||
\(415\) | −6.90092e11 | −1.14206 | ||||||||
\(416\) | −2.15250e11 | −0.352389 | ||||||||
\(417\) | 1.95955e11 | 0.317354 | ||||||||
\(418\) | −3.97962e11 | −0.637601 | ||||||||
\(419\) | −1.06755e12 | −1.69210 | −0.846048 | − | 0.533106i | \(-0.821025\pi\) | ||||
−0.846048 | + | 0.533106i | \(0.821025\pi\) | |||||||
\(420\) | 5.82891e11 | 0.914041 | ||||||||
\(421\) | 3.10696e11 | 0.482021 | 0.241011 | − | 0.970522i | \(-0.422521\pi\) | ||||
0.241011 | + | 0.970522i | \(0.422521\pi\) | |||||||
\(422\) | −8.59420e11 | −1.31917 | ||||||||
\(423\) | −3.48082e11 | −0.528628 | ||||||||
\(424\) | −1.33046e12 | −1.99919 | ||||||||
\(425\) | −6.81555e11 | −1.01333 | ||||||||
\(426\) | 7.74935e11 | 1.14004 | ||||||||
\(427\) | −5.33455e11 | −0.776555 | ||||||||
\(428\) | −5.25163e11 | −0.756480 | ||||||||
\(429\) | −5.05492e11 | −0.720537 | ||||||||
\(430\) | 1.57554e12 | 2.22239 | ||||||||
\(431\) | 2.59339e11 | 0.362010 | 0.181005 | − | 0.983482i | \(-0.442065\pi\) | ||||
0.181005 | + | 0.983482i | \(0.442065\pi\) | |||||||
\(432\) | 1.78065e11 | 0.245981 | ||||||||
\(433\) | −9.45969e11 | −1.29325 | −0.646624 | − | 0.762809i | \(-0.723820\pi\) | ||||
−0.646624 | + | 0.762809i | \(0.723820\pi\) | |||||||
\(434\) | 1.02737e12 | 1.39002 | ||||||||
\(435\) | −1.00705e12 | −1.34850 | ||||||||
\(436\) | 1.78983e12 | 2.37204 | ||||||||
\(437\) | 2.50810e11 | 0.328987 | ||||||||
\(438\) | 4.68876e11 | 0.608730 | ||||||||
\(439\) | −1.18489e12 | −1.52261 | −0.761306 | − | 0.648393i | \(-0.775441\pi\) | ||||
−0.761306 | + | 0.648393i | \(0.775441\pi\) | |||||||
\(440\) | −2.18549e12 | −2.77978 | ||||||||
\(441\) | −1.65744e11 | −0.208672 | ||||||||
\(442\) | 2.85063e12 | 3.55256 | ||||||||
\(443\) | −1.78010e11 | −0.219597 | −0.109799 | − | 0.993954i | \(-0.535021\pi\) | ||||
−0.109799 | + | 0.993954i | \(0.535021\pi\) | |||||||
\(444\) | 7.26316e11 | 0.886956 | ||||||||
\(445\) | 4.57853e9 | 0.00553485 | ||||||||
\(446\) | 7.43018e11 | 0.889185 | ||||||||
\(447\) | 3.09933e11 | 0.367184 | ||||||||
\(448\) | 3.63321e11 | 0.426127 | ||||||||
\(449\) | −2.46559e11 | −0.286294 | −0.143147 | − | 0.989701i | \(-0.545722\pi\) | ||||
−0.143147 | + | 0.989701i | \(0.545722\pi\) | |||||||
\(450\) | 2.72317e11 | 0.313054 | ||||||||
\(451\) | 1.10194e12 | 1.25419 | ||||||||
\(452\) | −1.15136e12 | −1.29744 | ||||||||
\(453\) | 8.46454e11 | 0.944412 | ||||||||
\(454\) | 1.31168e12 | 1.44903 | ||||||||
\(455\) | −7.37900e11 | −0.807136 | ||||||||
\(456\) | −3.16312e11 | −0.342590 | ||||||||
\(457\) | 5.95044e10 | 0.0638155 | 0.0319077 | − | 0.999491i | \(-0.489842\pi\) | ||||
0.0319077 | + | 0.999491i | \(0.489842\pi\) | |||||||
\(458\) | −3.57343e11 | −0.379482 | ||||||||
\(459\) | −3.47109e11 | −0.365014 | ||||||||
\(460\) | 2.64100e12 | 2.75016 | ||||||||
\(461\) | −7.50852e11 | −0.774284 | −0.387142 | − | 0.922020i | \(-0.626538\pi\) | ||||
−0.387142 | + | 0.922020i | \(0.626538\pi\) | |||||||
\(462\) | −7.11838e11 | −0.726930 | ||||||||
\(463\) | −3.64780e11 | −0.368907 | −0.184453 | − | 0.982841i | \(-0.559051\pi\) | ||||
−0.184453 | + | 0.982841i | \(0.559051\pi\) | |||||||
\(464\) | 2.40644e12 | 2.41015 | ||||||||
\(465\) | 9.32275e11 | 0.924710 | ||||||||
\(466\) | −5.41120e11 | −0.531566 | ||||||||
\(467\) | −8.88180e11 | −0.864122 | −0.432061 | − | 0.901844i | \(-0.642213\pi\) | ||||
−0.432061 | + | 0.901844i | \(0.642213\pi\) | |||||||
\(468\) | −7.70380e11 | −0.742333 | ||||||||
\(469\) | 9.35420e11 | 0.892748 | ||||||||
\(470\) | 3.65294e12 | 3.45305 | ||||||||
\(471\) | −7.62566e11 | −0.713975 | ||||||||
\(472\) | 2.68984e11 | 0.249452 | ||||||||
\(473\) | −1.30140e12 | −1.19546 | ||||||||
\(474\) | −1.31185e12 | −1.19367 | ||||||||
\(475\) | −1.83570e11 | −0.165455 | ||||||||
\(476\) | 2.71517e12 | 2.42419 | ||||||||
\(477\) | −3.93235e11 | −0.347792 | ||||||||
\(478\) | 4.42316e11 | 0.387531 | ||||||||
\(479\) | 1.10248e12 | 0.956886 | 0.478443 | − | 0.878119i | \(-0.341201\pi\) | ||||
0.478443 | + | 0.878119i | \(0.341201\pi\) | |||||||
\(480\) | −2.75060e11 | −0.236506 | ||||||||
\(481\) | −9.19466e11 | −0.783219 | ||||||||
\(482\) | 1.40798e12 | 1.18819 | ||||||||
\(483\) | 4.48626e11 | 0.375079 | ||||||||
\(484\) | 9.38155e11 | 0.777089 | ||||||||
\(485\) | −1.77571e12 | −1.45725 | ||||||||
\(486\) | 1.38689e11 | 0.112766 | ||||||||
\(487\) | −4.20755e11 | −0.338960 | −0.169480 | − | 0.985534i | \(-0.554209\pi\) | ||||
−0.169480 | + | 0.985534i | \(0.554209\pi\) | |||||||
\(488\) | 3.04824e12 | 2.43310 | ||||||||
\(489\) | 5.71006e11 | 0.451597 | ||||||||
\(490\) | 1.73940e12 | 1.36307 | ||||||||
\(491\) | −1.88333e12 | −1.46238 | −0.731188 | − | 0.682176i | \(-0.761034\pi\) | ||||
−0.731188 | + | 0.682176i | \(0.761034\pi\) | |||||||
\(492\) | 1.67938e12 | 1.29213 | ||||||||
\(493\) | −4.69098e12 | −3.57645 | ||||||||
\(494\) | 7.67791e11 | 0.580058 | ||||||||
\(495\) | −6.45951e11 | −0.483589 | ||||||||
\(496\) | −2.22775e12 | −1.65272 | ||||||||
\(497\) | −9.34397e11 | −0.686954 | ||||||||
\(498\) | 1.28437e12 | 0.935750 | ||||||||
\(499\) | −3.11715e11 | −0.225064 | −0.112532 | − | 0.993648i | \(-0.535896\pi\) | ||||
−0.112532 | + | 0.993648i | \(0.535896\pi\) | |||||||
\(500\) | 1.68500e12 | 1.20569 | ||||||||
\(501\) | −1.82092e11 | −0.129128 | ||||||||
\(502\) | −4.55980e12 | −3.20464 | ||||||||
\(503\) | 1.53038e12 | 1.06597 | 0.532984 | − | 0.846125i | \(-0.321071\pi\) | ||||
0.532984 | + | 0.846125i | \(0.321071\pi\) | |||||||
\(504\) | −5.65790e11 | −0.390587 | ||||||||
\(505\) | 3.04221e12 | 2.08151 | ||||||||
\(506\) | −3.22524e12 | −2.18718 | ||||||||
\(507\) | 1.16284e11 | 0.0781598 | ||||||||
\(508\) | 4.84873e12 | 3.23029 | ||||||||
\(509\) | −1.02987e12 | −0.680069 | −0.340035 | − | 0.940413i | \(-0.610439\pi\) | ||||
−0.340035 | + | 0.940413i | \(0.610439\pi\) | |||||||
\(510\) | 3.64273e12 | 2.38430 | ||||||||
\(511\) | −5.65360e11 | −0.366801 | ||||||||
\(512\) | −3.15084e12 | −2.02634 | ||||||||
\(513\) | −9.34905e10 | −0.0595991 | ||||||||
\(514\) | 2.29754e12 | 1.45188 | ||||||||
\(515\) | 3.34566e12 | 2.09580 | ||||||||
\(516\) | −1.98336e12 | −1.23162 | ||||||||
\(517\) | −3.01735e12 | −1.85746 | ||||||||
\(518\) | −1.29480e12 | −0.790168 | ||||||||
\(519\) | −1.33756e11 | −0.0809206 | ||||||||
\(520\) | 4.21647e12 | 2.52891 | ||||||||
\(521\) | −1.97364e11 | −0.117354 | −0.0586770 | − | 0.998277i | \(-0.518688\pi\) | ||||
−0.0586770 | + | 0.998277i | \(0.518688\pi\) | |||||||
\(522\) | 1.87429e12 | 1.10489 | ||||||||
\(523\) | 2.24605e12 | 1.31269 | 0.656344 | − | 0.754462i | \(-0.272102\pi\) | ||||
0.656344 | + | 0.754462i | \(0.272102\pi\) | |||||||
\(524\) | 1.89239e12 | 1.09653 | ||||||||
\(525\) | −3.28354e11 | −0.188636 | ||||||||
\(526\) | −1.05766e12 | −0.602438 | ||||||||
\(527\) | 4.34265e12 | 2.45249 | ||||||||
\(528\) | 1.54355e12 | 0.864309 | ||||||||
\(529\) | 2.31510e11 | 0.128535 | ||||||||
\(530\) | 4.12680e12 | 2.27181 | ||||||||
\(531\) | 7.95020e10 | 0.0433963 | ||||||||
\(532\) | 7.31306e11 | 0.395819 | ||||||||
\(533\) | −2.12598e12 | −1.14100 | ||||||||
\(534\) | −8.52140e9 | −0.00453498 | ||||||||
\(535\) | 8.49553e11 | 0.448331 | ||||||||
\(536\) | −5.34513e12 | −2.79716 | ||||||||
\(537\) | 2.52264e11 | 0.130909 | ||||||||
\(538\) | −1.41976e12 | −0.730627 | ||||||||
\(539\) | −1.43675e12 | −0.733218 | ||||||||
\(540\) | −9.84443e11 | −0.498217 | ||||||||
\(541\) | 1.79418e12 | 0.900490 | 0.450245 | − | 0.892905i | \(-0.351337\pi\) | ||||
0.450245 | + | 0.892905i | \(0.351337\pi\) | |||||||
\(542\) | 3.69672e11 | 0.184001 | ||||||||
\(543\) | −1.05090e12 | −0.518754 | ||||||||
\(544\) | −1.28126e12 | −0.627254 | ||||||||
\(545\) | −2.89539e12 | −1.40580 | ||||||||
\(546\) | 1.37335e12 | 0.661326 | ||||||||
\(547\) | 1.20032e12 | 0.573261 | 0.286631 | − | 0.958041i | \(-0.407465\pi\) | ||||
0.286631 | + | 0.958041i | \(0.407465\pi\) | |||||||
\(548\) | 6.01680e12 | 2.85005 | ||||||||
\(549\) | 9.00950e11 | 0.423278 | ||||||||
\(550\) | 2.36058e12 | 1.09999 | ||||||||
\(551\) | −1.26347e12 | −0.583959 | ||||||||
\(552\) | −2.56352e12 | −1.17520 | ||||||||
\(553\) | 1.58180e12 | 0.719264 | ||||||||
\(554\) | −2.04330e12 | −0.921593 | ||||||||
\(555\) | −1.17496e12 | −0.525658 | ||||||||
\(556\) | 2.58875e12 | 1.14883 | ||||||||
\(557\) | −1.07143e12 | −0.471646 | −0.235823 | − | 0.971796i | \(-0.575779\pi\) | ||||
−0.235823 | + | 0.971796i | \(0.575779\pi\) | |||||||
\(558\) | −1.73512e12 | −0.757661 | ||||||||
\(559\) | 2.51080e12 | 1.08757 | ||||||||
\(560\) | 2.25323e12 | 0.968187 | ||||||||
\(561\) | −3.00892e12 | −1.28256 | ||||||||
\(562\) | −5.80383e11 | −0.245415 | ||||||||
\(563\) | −4.60836e12 | −1.93312 | −0.966559 | − | 0.256444i | \(-0.917449\pi\) | ||||
−0.966559 | + | 0.256444i | \(0.917449\pi\) | |||||||
\(564\) | −4.59850e12 | −1.91364 | ||||||||
\(565\) | 1.86254e12 | 0.768933 | ||||||||
\(566\) | −6.10151e11 | −0.249899 | ||||||||
\(567\) | −1.67227e11 | −0.0679490 | ||||||||
\(568\) | 5.33928e12 | 2.15236 | ||||||||
\(569\) | −3.75584e12 | −1.50211 | −0.751055 | − | 0.660240i | \(-0.770454\pi\) | ||||
−0.751055 | + | 0.660240i | \(0.770454\pi\) | |||||||
\(570\) | 9.81135e11 | 0.389307 | ||||||||
\(571\) | 3.33077e12 | 1.31124 | 0.655620 | − | 0.755091i | \(-0.272407\pi\) | ||||
0.655620 | + | 0.755091i | \(0.272407\pi\) | |||||||
\(572\) | −6.67804e12 | −2.60835 | ||||||||
\(573\) | 1.11217e12 | 0.430997 | ||||||||
\(574\) | −2.99382e12 | −1.15112 | ||||||||
\(575\) | −1.48772e12 | −0.567567 | ||||||||
\(576\) | −6.13612e11 | −0.232270 | ||||||||
\(577\) | −2.06344e12 | −0.774998 | −0.387499 | − | 0.921870i | \(-0.626661\pi\) | ||||
−0.387499 | + | 0.921870i | \(0.626661\pi\) | |||||||
\(578\) | 1.22514e13 | 4.56573 | ||||||||
\(579\) | 2.91557e12 | 1.07813 | ||||||||
\(580\) | −1.33042e13 | −4.88159 | ||||||||
\(581\) | −1.54867e12 | −0.563853 | ||||||||
\(582\) | 3.30488e12 | 1.19399 | ||||||||
\(583\) | −3.40876e12 | −1.22205 | ||||||||
\(584\) | 3.23055e12 | 1.14926 | ||||||||
\(585\) | 1.24624e12 | 0.439946 | ||||||||
\(586\) | −3.67017e12 | −1.28572 | ||||||||
\(587\) | −1.53457e12 | −0.533476 | −0.266738 | − | 0.963769i | \(-0.585946\pi\) | ||||
−0.266738 | + | 0.963769i | \(0.585946\pi\) | |||||||
\(588\) | −2.18964e12 | −0.755397 | ||||||||
\(589\) | 1.16965e12 | 0.400440 | ||||||||
\(590\) | −8.34332e11 | −0.283469 | ||||||||
\(591\) | −2.52033e12 | −0.849795 | ||||||||
\(592\) | 2.80765e12 | 0.939498 | ||||||||
\(593\) | −9.77682e11 | −0.324677 | −0.162338 | − | 0.986735i | \(-0.551904\pi\) | ||||
−0.162338 | + | 0.986735i | \(0.551904\pi\) | |||||||
\(594\) | 1.20222e12 | 0.396228 | ||||||||
\(595\) | −4.39232e12 | −1.43670 | ||||||||
\(596\) | 4.09451e12 | 1.32921 | ||||||||
\(597\) | −2.15558e12 | −0.694513 | ||||||||
\(598\) | 6.22248e12 | 1.98979 | ||||||||
\(599\) | 1.37554e11 | 0.0436569 | 0.0218284 | − | 0.999762i | \(-0.493051\pi\) | ||||
0.0218284 | + | 0.999762i | \(0.493051\pi\) | |||||||
\(600\) | 1.87626e12 | 0.591034 | ||||||||
\(601\) | 2.24306e12 | 0.701303 | 0.350652 | − | 0.936506i | \(-0.385960\pi\) | ||||
0.350652 | + | 0.936506i | \(0.385960\pi\) | |||||||
\(602\) | 3.53573e12 | 1.09722 | ||||||||
\(603\) | −1.57983e12 | −0.486611 | ||||||||
\(604\) | 1.11825e13 | 3.41879 | ||||||||
\(605\) | −1.51765e12 | −0.460544 | ||||||||
\(606\) | −5.66205e12 | −1.70548 | ||||||||
\(607\) | −4.73786e11 | −0.141655 | −0.0708277 | − | 0.997489i | \(-0.522564\pi\) | ||||
−0.0708277 | + | 0.997489i | \(0.522564\pi\) | |||||||
\(608\) | −3.45096e11 | −0.102417 | ||||||||
\(609\) | −2.25998e12 | −0.665773 | ||||||||
\(610\) | −9.45501e12 | −2.76489 | ||||||||
\(611\) | 5.82139e12 | 1.68982 | ||||||||
\(612\) | −4.58565e12 | −1.32135 | ||||||||
\(613\) | −2.21574e12 | −0.633793 | −0.316896 | − | 0.948460i | \(-0.602641\pi\) | ||||
−0.316896 | + | 0.948460i | \(0.602641\pi\) | |||||||
\(614\) | −3.57811e12 | −1.01601 | ||||||||
\(615\) | −2.71672e12 | −0.765784 | ||||||||
\(616\) | −4.90455e12 | −1.37242 | ||||||||
\(617\) | −2.79669e12 | −0.776894 | −0.388447 | − | 0.921471i | \(-0.626988\pi\) | ||||
−0.388447 | + | 0.921471i | \(0.626988\pi\) | |||||||
\(618\) | −6.22682e12 | −1.71719 | ||||||||
\(619\) | 5.88609e12 | 1.61146 | 0.805729 | − | 0.592285i | \(-0.201774\pi\) | ||||
0.805729 | + | 0.592285i | \(0.201774\pi\) | |||||||
\(620\) | 1.23163e13 | 3.34747 | ||||||||
\(621\) | −7.57683e11 | −0.204445 | ||||||||
\(622\) | −4.63483e12 | −1.24159 | ||||||||
\(623\) | 1.02749e10 | 0.00273263 | ||||||||
\(624\) | −2.97799e12 | −0.786307 | ||||||||
\(625\) | −4.76389e12 | −1.24883 | ||||||||
\(626\) | 5.01234e12 | 1.30454 | ||||||||
\(627\) | −8.10423e11 | −0.209415 | ||||||||
\(628\) | −1.00742e13 | −2.58460 | ||||||||
\(629\) | −5.47308e12 | −1.39413 | ||||||||
\(630\) | 1.75496e12 | 0.443849 | ||||||||
\(631\) | −1.73807e11 | −0.0436451 | −0.0218225 | − | 0.999762i | \(-0.506947\pi\) | ||||
−0.0218225 | + | 0.999762i | \(0.506947\pi\) | |||||||
\(632\) | −9.03864e12 | −2.25360 | ||||||||
\(633\) | −1.75015e12 | −0.433270 | ||||||||
\(634\) | 6.76269e12 | 1.66233 | ||||||||
\(635\) | −7.84376e12 | −1.91444 | ||||||||
\(636\) | −5.19502e12 | −1.25901 | ||||||||
\(637\) | 2.77194e12 | 0.667047 | ||||||||
\(638\) | 1.62473e13 | 3.88229 | ||||||||
\(639\) | 1.57810e12 | 0.374439 | ||||||||
\(640\) | 8.17819e12 | 1.92685 | ||||||||
\(641\) | 3.58625e12 | 0.839034 | 0.419517 | − | 0.907748i | \(-0.362199\pi\) | ||||
0.419517 | + | 0.907748i | \(0.362199\pi\) | |||||||
\(642\) | −1.58116e12 | −0.367339 | ||||||||
\(643\) | −4.38236e12 | −1.01102 | −0.505509 | − | 0.862821i | \(-0.668695\pi\) | ||||
−0.505509 | + | 0.862821i | \(0.668695\pi\) | |||||||
\(644\) | 5.92679e12 | 1.35779 | ||||||||
\(645\) | 3.20847e12 | 0.729927 | ||||||||
\(646\) | 4.57024e12 | 1.03251 | ||||||||
\(647\) | 8.09880e11 | 0.181699 | 0.0908493 | − | 0.995865i | \(-0.471042\pi\) | ||||
0.0908493 | + | 0.995865i | \(0.471042\pi\) | |||||||
\(648\) | 9.55561e11 | 0.212898 | ||||||||
\(649\) | 6.89163e11 | 0.152483 | ||||||||
\(650\) | −4.55428e12 | −1.00071 | ||||||||
\(651\) | 2.09216e12 | 0.456542 | ||||||||
\(652\) | 7.54355e12 | 1.63479 | ||||||||
\(653\) | −6.63384e12 | −1.42776 | −0.713880 | − | 0.700268i | \(-0.753064\pi\) | ||||
−0.713880 | + | 0.700268i | \(0.753064\pi\) | |||||||
\(654\) | 5.38880e12 | 1.15184 | ||||||||
\(655\) | −3.06131e12 | −0.649862 | ||||||||
\(656\) | 6.49182e12 | 1.36867 | ||||||||
\(657\) | 9.54834e11 | 0.199933 | ||||||||
\(658\) | 8.19774e12 | 1.70482 | ||||||||
\(659\) | 6.81084e12 | 1.40675 | 0.703374 | − | 0.710820i | \(-0.251676\pi\) | ||||
0.703374 | + | 0.710820i | \(0.251676\pi\) | |||||||
\(660\) | −8.53364e12 | −1.75060 | ||||||||
\(661\) | −7.93016e12 | −1.61575 | −0.807877 | − | 0.589351i | \(-0.799383\pi\) | ||||
−0.807877 | + | 0.589351i | \(0.799383\pi\) | |||||||
\(662\) | −1.17957e13 | −2.38706 | ||||||||
\(663\) | 5.80512e12 | 1.16681 | ||||||||
\(664\) | 8.84932e12 | 1.76666 | ||||||||
\(665\) | −1.18303e12 | −0.234584 | ||||||||
\(666\) | 2.18679e12 | 0.430697 | ||||||||
\(667\) | −1.02396e13 | −2.00317 | ||||||||
\(668\) | −2.40561e12 | −0.467446 | ||||||||
\(669\) | 1.51310e12 | 0.292046 | ||||||||
\(670\) | 1.65795e13 | 3.17859 | ||||||||
\(671\) | 7.80989e12 | 1.48728 | ||||||||
\(672\) | −6.17276e11 | −0.116766 | ||||||||
\(673\) | 8.46361e11 | 0.159033 | 0.0795166 | − | 0.996834i | \(-0.474662\pi\) | ||||
0.0795166 | + | 0.996834i | \(0.474662\pi\) | |||||||
\(674\) | −3.38818e12 | −0.632408 | ||||||||
\(675\) | 5.54555e11 | 0.102820 | ||||||||
\(676\) | 1.53622e12 | 0.282940 | ||||||||
\(677\) | 7.18796e12 | 1.31509 | 0.657546 | − | 0.753414i | \(-0.271594\pi\) | ||||
0.657546 | + | 0.753414i | \(0.271594\pi\) | |||||||
\(678\) | −3.46650e12 | −0.630025 | ||||||||
\(679\) | −3.98494e12 | −0.719462 | ||||||||
\(680\) | 2.50984e13 | 4.50148 | ||||||||
\(681\) | 2.67115e12 | 0.475923 | ||||||||
\(682\) | −1.50409e13 | −2.66221 | ||||||||
\(683\) | 2.97182e12 | 0.522552 | 0.261276 | − | 0.965264i | \(-0.415857\pi\) | ||||
0.261276 | + | 0.965264i | \(0.415857\pi\) | |||||||
\(684\) | −1.23510e12 | −0.215750 | ||||||||
\(685\) | −9.73333e12 | −1.68909 | ||||||||
\(686\) | 1.01389e13 | 1.74796 | ||||||||
\(687\) | −7.27705e11 | −0.124638 | ||||||||
\(688\) | −7.66690e12 | −1.30458 | ||||||||
\(689\) | 6.57654e12 | 1.11176 | ||||||||
\(690\) | 7.95150e12 | 1.33545 | ||||||||
\(691\) | 1.95699e12 | 0.326541 | 0.163271 | − | 0.986581i | \(-0.447796\pi\) | ||||
0.163271 | + | 0.986581i | \(0.447796\pi\) | |||||||
\(692\) | −1.76704e12 | −0.292934 | ||||||||
\(693\) | −1.44961e12 | −0.238754 | ||||||||
\(694\) | −9.84102e12 | −1.61036 | ||||||||
\(695\) | −4.18781e12 | −0.680856 | ||||||||
\(696\) | 1.29138e13 | 2.08600 | ||||||||
\(697\) | −1.26548e13 | −2.03099 | ||||||||
\(698\) | 9.19561e12 | 1.46633 | ||||||||
\(699\) | −1.10195e12 | −0.174589 | ||||||||
\(700\) | −4.33787e12 | −0.682865 | ||||||||
\(701\) | −1.67805e12 | −0.262467 | −0.131234 | − | 0.991351i | \(-0.541894\pi\) | ||||
−0.131234 | + | 0.991351i | \(0.541894\pi\) | |||||||
\(702\) | −2.31945e12 | −0.360470 | ||||||||
\(703\) | −1.47412e12 | −0.227633 | ||||||||
\(704\) | −5.31909e12 | −0.816133 | ||||||||
\(705\) | 7.43896e12 | 1.13413 | ||||||||
\(706\) | 1.30690e13 | 1.97980 | ||||||||
\(707\) | 6.82716e12 | 1.02767 | ||||||||
\(708\) | 1.05030e12 | 0.157095 | ||||||||
\(709\) | −6.62647e12 | −0.984860 | −0.492430 | − | 0.870352i | \(-0.663891\pi\) | ||||
−0.492430 | + | 0.870352i | \(0.663891\pi\) | |||||||
\(710\) | −1.65613e13 | −2.44587 | ||||||||
\(711\) | −2.67150e12 | −0.392050 | ||||||||
\(712\) | −5.87123e10 | −0.00856188 | ||||||||
\(713\) | 9.47929e12 | 1.37364 | ||||||||
\(714\) | 8.17483e12 | 1.17716 | ||||||||
\(715\) | 1.08030e13 | 1.54585 | ||||||||
\(716\) | 3.33265e12 | 0.473894 | ||||||||
\(717\) | 9.00746e11 | 0.127282 | ||||||||
\(718\) | −9.76733e12 | −1.37156 | ||||||||
\(719\) | 2.94579e12 | 0.411076 | 0.205538 | − | 0.978649i | \(-0.434106\pi\) | ||||
0.205538 | + | 0.978649i | \(0.434106\pi\) | |||||||
\(720\) | −3.80547e12 | −0.527730 | ||||||||
\(721\) | 7.50815e12 | 1.03472 | ||||||||
\(722\) | −1.16041e13 | −1.58926 | ||||||||
\(723\) | 2.86726e12 | 0.390252 | ||||||||
\(724\) | −1.38834e13 | −1.87790 | ||||||||
\(725\) | 7.49449e12 | 1.00744 | ||||||||
\(726\) | 2.82459e12 | 0.377347 | ||||||||
\(727\) | 2.39601e12 | 0.318114 | 0.159057 | − | 0.987269i | \(-0.449155\pi\) | ||||
0.159057 | + | 0.987269i | \(0.449155\pi\) | |||||||
\(728\) | 9.46238e12 | 1.24856 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | −1.00205e13 | −1.30598 | ||||||||
\(731\) | 1.49454e13 | 1.93589 | ||||||||
\(732\) | 1.19024e13 | 1.53227 | ||||||||
\(733\) | 1.44611e13 | 1.85026 | 0.925130 | − | 0.379651i | \(-0.123956\pi\) | ||||
0.925130 | + | 0.379651i | \(0.123956\pi\) | |||||||
\(734\) | −3.66630e12 | −0.466225 | ||||||||
\(735\) | 3.54217e12 | 0.447689 | ||||||||
\(736\) | −2.79679e12 | −0.351326 | ||||||||
\(737\) | −1.36947e13 | −1.70982 | ||||||||
\(738\) | 5.05626e12 | 0.627445 | ||||||||
\(739\) | 3.45079e12 | 0.425616 | 0.212808 | − | 0.977094i | \(-0.431739\pi\) | ||||
0.212808 | + | 0.977094i | \(0.431739\pi\) | |||||||
\(740\) | −1.55223e13 | −1.90289 | ||||||||
\(741\) | 1.56355e12 | 0.190516 | ||||||||
\(742\) | 9.26114e12 | 1.12162 | ||||||||
\(743\) | −1.49532e13 | −1.80005 | −0.900025 | − | 0.435839i | \(-0.856452\pi\) | ||||
−0.900025 | + | 0.435839i | \(0.856452\pi\) | |||||||
\(744\) | −1.19549e13 | −1.43044 | ||||||||
\(745\) | −6.62366e12 | −0.787762 | ||||||||
\(746\) | −2.91775e13 | −3.44924 | ||||||||
\(747\) | 2.61554e12 | 0.307340 | ||||||||
\(748\) | −3.97507e13 | −4.64288 | ||||||||
\(749\) | 1.90652e12 | 0.221347 | ||||||||
\(750\) | 5.07320e12 | 0.585472 | ||||||||
\(751\) | −9.02826e12 | −1.03568 | −0.517839 | − | 0.855478i | \(-0.673263\pi\) | ||||
−0.517839 | + | 0.855478i | \(0.673263\pi\) | |||||||
\(752\) | −1.77760e13 | −2.02700 | ||||||||
\(753\) | −9.28572e12 | −1.05254 | ||||||||
\(754\) | −3.13460e13 | −3.53193 | ||||||||
\(755\) | −1.80898e13 | −2.02616 | ||||||||
\(756\) | −2.20923e12 | −0.245976 | ||||||||
\(757\) | 5.66897e11 | 0.0627441 | 0.0313720 | − | 0.999508i | \(-0.490012\pi\) | ||||
0.0313720 | + | 0.999508i | \(0.490012\pi\) | |||||||
\(758\) | 5.72666e12 | 0.630072 | ||||||||
\(759\) | −6.56798e12 | −0.718363 | ||||||||
\(760\) | 6.76000e12 | 0.734997 | ||||||||
\(761\) | 4.14422e12 | 0.447932 | 0.223966 | − | 0.974597i | \(-0.428100\pi\) | ||||
0.223966 | + | 0.974597i | \(0.428100\pi\) | |||||||
\(762\) | 1.45985e13 | 1.56860 | ||||||||
\(763\) | −6.49769e12 | −0.694062 | ||||||||
\(764\) | 1.46928e13 | 1.56022 | ||||||||
\(765\) | 7.41817e12 | 0.783106 | ||||||||
\(766\) | −6.26894e12 | −0.657907 | ||||||||
\(767\) | −1.32961e12 | −0.138722 | ||||||||
\(768\) | −1.13423e13 | −1.17646 | ||||||||
\(769\) | 1.43841e13 | 1.48325 | 0.741623 | − | 0.670817i | \(-0.234056\pi\) | ||||
0.741623 | + | 0.670817i | \(0.234056\pi\) | |||||||
\(770\) | 1.52129e13 | 1.55957 | ||||||||
\(771\) | 4.67879e12 | 0.476858 | ||||||||
\(772\) | 3.85175e13 | 3.90284 | ||||||||
\(773\) | −1.23525e13 | −1.24436 | −0.622180 | − | 0.782874i | \(-0.713753\pi\) | ||||
−0.622180 | + | 0.782874i | \(0.713753\pi\) | |||||||
\(774\) | −5.97149e12 | −0.598065 | ||||||||
\(775\) | −6.93798e12 | −0.690837 | ||||||||
\(776\) | 2.27706e13 | 2.25422 | ||||||||
\(777\) | −2.63677e12 | −0.259524 | ||||||||
\(778\) | 1.68405e13 | 1.64796 | ||||||||
\(779\) | −3.40844e12 | −0.331618 | ||||||||
\(780\) | 1.64640e13 | 1.59261 | ||||||||
\(781\) | 1.36798e13 | 1.31568 | ||||||||
\(782\) | 3.70390e13 | 3.54184 | ||||||||
\(783\) | 3.81687e12 | 0.362894 | ||||||||
\(784\) | −8.46431e12 | −0.800146 | ||||||||
\(785\) | 1.62970e13 | 1.53177 | ||||||||
\(786\) | 5.69760e12 | 0.532464 | ||||||||
\(787\) | −9.90204e12 | −0.920107 | −0.460053 | − | 0.887891i | \(-0.652170\pi\) | ||||
−0.460053 | + | 0.887891i | \(0.652170\pi\) | |||||||
\(788\) | −3.32961e13 | −3.07627 | ||||||||
\(789\) | −2.15386e12 | −0.197866 | ||||||||
\(790\) | 2.80360e13 | 2.56091 | ||||||||
\(791\) | 4.17982e12 | 0.379633 | ||||||||
\(792\) | 8.28328e12 | 0.748065 | ||||||||
\(793\) | −1.50677e13 | −1.35306 | ||||||||
\(794\) | −1.58153e13 | −1.41217 | ||||||||
\(795\) | 8.40394e12 | 0.746158 | ||||||||
\(796\) | −2.84774e13 | −2.51415 | ||||||||
\(797\) | −2.10226e13 | −1.84554 | −0.922769 | − | 0.385353i | \(-0.874080\pi\) | ||||
−0.922769 | + | 0.385353i | \(0.874080\pi\) | |||||||
\(798\) | 2.20181e12 | 0.192206 | ||||||||
\(799\) | 3.46516e13 | 3.00789 | ||||||||
\(800\) | 2.04700e12 | 0.176690 | ||||||||
\(801\) | −1.73532e10 | −0.00148948 | ||||||||
\(802\) | −1.57711e13 | −1.34610 | ||||||||
\(803\) | 8.27698e12 | 0.702509 | ||||||||
\(804\) | −2.08711e13 | −1.76154 | ||||||||
\(805\) | −9.58772e12 | −0.804700 | ||||||||
\(806\) | 2.90184e13 | 2.42196 | ||||||||
\(807\) | −2.89125e12 | −0.239969 | ||||||||
\(808\) | −3.90114e13 | −3.21989 | ||||||||
\(809\) | 9.92457e12 | 0.814598 | 0.407299 | − | 0.913295i | \(-0.366471\pi\) | ||||
0.407299 | + | 0.913295i | \(0.366471\pi\) | |||||||
\(810\) | −2.96395e12 | −0.241929 | ||||||||
\(811\) | 2.08737e13 | 1.69436 | 0.847180 | − | 0.531306i | \(-0.178299\pi\) | ||||
0.847180 | + | 0.531306i | \(0.178299\pi\) | |||||||
\(812\) | −2.98565e13 | −2.41011 | ||||||||
\(813\) | 7.52811e11 | 0.0604336 | ||||||||
\(814\) | 1.89562e13 | 1.51335 | ||||||||
\(815\) | −1.22031e13 | −0.968863 | ||||||||
\(816\) | −1.77263e13 | −1.39963 | ||||||||
\(817\) | 4.02541e12 | 0.316090 | ||||||||
\(818\) | 2.29076e13 | 1.78892 | ||||||||
\(819\) | 2.79674e12 | 0.217207 | ||||||||
\(820\) | −3.58905e13 | −2.77215 | ||||||||
\(821\) | −5.79690e12 | −0.445299 | −0.222649 | − | 0.974899i | \(-0.571471\pi\) | ||||
−0.222649 | + | 0.974899i | \(0.571471\pi\) | |||||||
\(822\) | 1.81153e13 | 1.38396 | ||||||||
\(823\) | −5.11028e12 | −0.388280 | −0.194140 | − | 0.980974i | \(-0.562192\pi\) | ||||
−0.194140 | + | 0.980974i | \(0.562192\pi\) | |||||||
\(824\) | −4.29027e13 | −3.24199 | ||||||||
\(825\) | 4.80716e12 | 0.361282 | ||||||||
\(826\) | −1.87236e12 | −0.139952 | ||||||||
\(827\) | −1.38342e13 | −1.02844 | −0.514222 | − | 0.857657i | \(-0.671919\pi\) | ||||
−0.514222 | + | 0.857657i | \(0.671919\pi\) | |||||||
\(828\) | −1.00097e13 | −0.740092 | ||||||||
\(829\) | 1.98846e13 | 1.46225 | 0.731125 | − | 0.682244i | \(-0.238996\pi\) | ||||
0.731125 | + | 0.682244i | \(0.238996\pi\) | |||||||
\(830\) | −2.74487e13 | −2.00757 | ||||||||
\(831\) | −4.16105e12 | −0.302690 | ||||||||
\(832\) | 1.02622e13 | 0.742478 | ||||||||
\(833\) | 1.64998e13 | 1.18735 | ||||||||
\(834\) | 7.79420e12 | 0.557859 | ||||||||
\(835\) | 3.89154e12 | 0.277034 | ||||||||
\(836\) | −1.07065e13 | −0.758085 | ||||||||
\(837\) | −3.53345e12 | −0.248848 | ||||||||
\(838\) | −4.24623e13 | −2.97444 | ||||||||
\(839\) | −2.27812e12 | −0.158726 | −0.0793629 | − | 0.996846i | \(-0.525289\pi\) | ||||
−0.0793629 | + | 0.996846i | \(0.525289\pi\) | |||||||
\(840\) | 1.20917e13 | 0.837972 | ||||||||
\(841\) | 3.70756e13 | 2.55568 | ||||||||
\(842\) | 1.23581e13 | 0.847318 | ||||||||
\(843\) | −1.18191e12 | −0.0806047 | ||||||||
\(844\) | −2.31212e13 | −1.56844 | ||||||||
\(845\) | −2.48514e12 | −0.167685 | ||||||||
\(846\) | −1.38451e13 | −0.929246 | ||||||||
\(847\) | −3.40582e12 | −0.227377 | ||||||||
\(848\) | −2.00819e13 | −1.33359 | ||||||||
\(849\) | −1.24253e12 | −0.0820772 | ||||||||
\(850\) | −2.71092e13 | −1.78128 | ||||||||
\(851\) | −1.19469e13 | −0.780855 | ||||||||
\(852\) | 2.08482e13 | 1.35547 | ||||||||
\(853\) | −7.01843e12 | −0.453910 | −0.226955 | − | 0.973905i | \(-0.572877\pi\) | ||||
−0.226955 | + | 0.973905i | \(0.572877\pi\) | |||||||
\(854\) | −2.12184e13 | −1.36506 | ||||||||
\(855\) | 1.99801e12 | 0.127865 | ||||||||
\(856\) | −1.08941e13 | −0.693523 | ||||||||
\(857\) | 2.61156e12 | 0.165381 | 0.0826905 | − | 0.996575i | \(-0.473649\pi\) | ||||
0.0826905 | + | 0.996575i | \(0.473649\pi\) | |||||||
\(858\) | −2.01062e13 | −1.26659 | ||||||||
\(859\) | −1.25048e13 | −0.783624 | −0.391812 | − | 0.920045i | \(-0.628152\pi\) | ||||
−0.391812 | + | 0.920045i | \(0.628152\pi\) | |||||||
\(860\) | 4.23870e13 | 2.64235 | ||||||||
\(861\) | −6.09671e12 | −0.378078 | ||||||||
\(862\) | 1.03153e13 | 0.636357 | ||||||||
\(863\) | −1.54530e13 | −0.948338 | −0.474169 | − | 0.880434i | \(-0.657252\pi\) | ||||
−0.474169 | + | 0.880434i | \(0.657252\pi\) | |||||||
\(864\) | 1.04252e12 | 0.0636459 | ||||||||
\(865\) | 2.85853e12 | 0.173608 | ||||||||
\(866\) | −3.76264e13 | −2.27333 | ||||||||
\(867\) | 2.49491e13 | 1.49958 | ||||||||
\(868\) | 2.76395e13 | 1.65269 | ||||||||
\(869\) | −2.31579e13 | −1.37756 | ||||||||
\(870\) | −4.00561e13 | −2.37045 | ||||||||
\(871\) | 2.64213e13 | 1.55551 | ||||||||
\(872\) | 3.71288e13 | 2.17463 | ||||||||
\(873\) | 6.73016e12 | 0.392158 | ||||||||
\(874\) | 9.97610e12 | 0.578308 | ||||||||
\(875\) | −6.11714e12 | −0.352787 | ||||||||
\(876\) | 1.26143e13 | 0.723759 | ||||||||
\(877\) | 3.17085e13 | 1.80999 | 0.904997 | − | 0.425417i | \(-0.139873\pi\) | ||||
0.904997 | + | 0.425417i | \(0.139873\pi\) | |||||||
\(878\) | −4.71297e13 | −2.67651 | ||||||||
\(879\) | −7.47405e12 | −0.422285 | ||||||||
\(880\) | −3.29877e13 | −1.85430 | ||||||||
\(881\) | 2.45926e13 | 1.37535 | 0.687673 | − | 0.726020i | \(-0.258632\pi\) | ||||
0.687673 | + | 0.726020i | \(0.258632\pi\) | |||||||
\(882\) | −6.59256e12 | −0.366814 | ||||||||
\(883\) | 1.49981e13 | 0.830257 | 0.415128 | − | 0.909763i | \(-0.363737\pi\) | ||||
0.415128 | + | 0.909763i | \(0.363737\pi\) | |||||||
\(884\) | 7.66913e13 | 4.22387 | ||||||||
\(885\) | −1.69906e12 | −0.0931031 | ||||||||
\(886\) | −7.08043e12 | −0.386018 | ||||||||
\(887\) | −1.14485e13 | −0.620999 | −0.310500 | − | 0.950574i | \(-0.600496\pi\) | ||||
−0.310500 | + | 0.950574i | \(0.600496\pi\) | |||||||
\(888\) | 1.50669e13 | 0.813141 | ||||||||
\(889\) | −1.76025e13 | −0.945186 | ||||||||
\(890\) | 1.82113e11 | 0.00972941 | ||||||||
\(891\) | 2.44824e12 | 0.130138 | ||||||||
\(892\) | 1.99896e13 | 1.05721 | ||||||||
\(893\) | 9.33307e12 | 0.491126 | ||||||||
\(894\) | 1.23277e13 | 0.645452 | ||||||||
\(895\) | −5.39121e12 | −0.280855 | ||||||||
\(896\) | 1.83531e13 | 0.951311 | ||||||||
\(897\) | 1.26716e13 | 0.653532 | ||||||||
\(898\) | −9.80700e12 | −0.503260 | ||||||||
\(899\) | −4.77524e13 | −2.43824 | ||||||||
\(900\) | 7.32621e12 | 0.372210 | ||||||||
\(901\) | 3.91465e13 | 1.97894 | ||||||||
\(902\) | 4.38302e13 | 2.20467 | ||||||||
\(903\) | 7.20028e12 | 0.360375 | ||||||||
\(904\) | −2.38841e13 | −1.18946 | ||||||||
\(905\) | 2.24590e13 | 1.11294 | ||||||||
\(906\) | 3.36681e13 | 1.66013 | ||||||||
\(907\) | −1.35483e12 | −0.0664740 | −0.0332370 | − | 0.999447i | \(-0.510582\pi\) | ||||
−0.0332370 | + | 0.999447i | \(0.510582\pi\) | |||||||
\(908\) | 3.52885e13 | 1.72285 | ||||||||
\(909\) | −1.15304e13 | −0.560152 | ||||||||
\(910\) | −2.93503e13 | −1.41882 | ||||||||
\(911\) | −1.98115e13 | −0.952984 | −0.476492 | − | 0.879179i | \(-0.658092\pi\) | ||||
−0.476492 | + | 0.879179i | \(0.658092\pi\) | |||||||
\(912\) | −4.77442e12 | −0.228530 | ||||||||
\(913\) | 2.26728e13 | 1.07991 | ||||||||
\(914\) | 2.36681e12 | 0.112178 | ||||||||
\(915\) | −1.92545e13 | −0.908106 | ||||||||
\(916\) | −9.61369e12 | −0.451191 | ||||||||
\(917\) | −6.87002e12 | −0.320846 | ||||||||
\(918\) | −1.38064e13 | −0.641637 | ||||||||
\(919\) | −3.57149e12 | −0.165169 | −0.0825847 | − | 0.996584i | \(-0.526318\pi\) | ||||
−0.0825847 | + | 0.996584i | \(0.526318\pi\) | |||||||
\(920\) | 5.47857e13 | 2.52128 | ||||||||
\(921\) | −7.28658e12 | −0.333699 | ||||||||
\(922\) | −2.98655e13 | −1.36107 | ||||||||
\(923\) | −2.63924e13 | −1.19694 | ||||||||
\(924\) | −1.91507e13 | −0.864295 | ||||||||
\(925\) | 8.74401e12 | 0.392711 | ||||||||
\(926\) | −1.45093e13 | −0.648481 | ||||||||
\(927\) | −1.26805e13 | −0.563997 | ||||||||
\(928\) | 1.40890e13 | 0.623611 | ||||||||
\(929\) | −3.50882e13 | −1.54557 | −0.772787 | − | 0.634665i | \(-0.781138\pi\) | ||||
−0.772787 | + | 0.634665i | \(0.781138\pi\) | |||||||
\(930\) | 3.70817e13 | 1.62550 | ||||||||
\(931\) | 4.44407e12 | 0.193869 | ||||||||
\(932\) | −1.45579e13 | −0.632013 | ||||||||
\(933\) | −9.43850e12 | −0.407789 | ||||||||
\(934\) | −3.53278e13 | −1.51899 | ||||||||
\(935\) | 6.43044e13 | 2.75162 | ||||||||
\(936\) | −1.59810e13 | −0.680553 | ||||||||
\(937\) | 3.73196e13 | 1.58164 | 0.790822 | − | 0.612047i | \(-0.209653\pi\) | ||||
0.790822 | + | 0.612047i | \(0.209653\pi\) | |||||||
\(938\) | 3.72068e13 | 1.56931 | ||||||||
\(939\) | 1.02073e13 | 0.428465 | ||||||||
\(940\) | 9.82759e13 | 4.10555 | ||||||||
\(941\) | −6.95147e12 | −0.289017 | −0.144508 | − | 0.989504i | \(-0.546160\pi\) | ||||
−0.144508 | + | 0.989504i | \(0.546160\pi\) | |||||||
\(942\) | −3.03314e13 | −1.25506 | ||||||||
\(943\) | −2.76233e13 | −1.13756 | ||||||||
\(944\) | 4.06004e12 | 0.166401 | ||||||||
\(945\) | 3.57386e12 | 0.145779 | ||||||||
\(946\) | −5.17638e13 | −2.10144 | ||||||||
\(947\) | 1.32678e12 | 0.0536071 | 0.0268036 | − | 0.999641i | \(-0.491467\pi\) | ||||
0.0268036 | + | 0.999641i | \(0.491467\pi\) | |||||||
\(948\) | −3.52931e13 | −1.41923 | ||||||||
\(949\) | −1.59688e13 | −0.639109 | ||||||||
\(950\) | −7.30159e12 | −0.290845 | ||||||||
\(951\) | 1.37718e13 | 0.545980 | ||||||||
\(952\) | 5.63244e13 | 2.22244 | ||||||||
\(953\) | −6.00433e12 | −0.235802 | −0.117901 | − | 0.993025i | \(-0.537616\pi\) | ||||
−0.117901 | + | 0.993025i | \(0.537616\pi\) | |||||||
\(954\) | −1.56411e13 | −0.611364 | ||||||||
\(955\) | −2.37685e13 | −0.924668 | ||||||||
\(956\) | 1.18997e13 | 0.460762 | ||||||||
\(957\) | 3.30865e13 | 1.27511 | ||||||||
\(958\) | 4.38516e13 | 1.68206 | ||||||||
\(959\) | −2.18430e13 | −0.833929 | ||||||||
\(960\) | 1.31137e13 | 0.498315 | ||||||||
\(961\) | 1.77669e13 | 0.671981 | ||||||||
\(962\) | −3.65722e13 | −1.37678 | ||||||||
\(963\) | −3.21992e12 | −0.120650 | ||||||||
\(964\) | 3.78793e13 | 1.41272 | ||||||||
\(965\) | −6.23095e13 | −2.31303 | ||||||||
\(966\) | 1.78443e13 | 0.659330 | ||||||||
\(967\) | −7.02355e12 | −0.258308 | −0.129154 | − | 0.991625i | \(-0.541226\pi\) | ||||
−0.129154 | + | 0.991625i | \(0.541226\pi\) | |||||||
\(968\) | 1.94614e13 | 0.712417 | ||||||||
\(969\) | 9.30698e12 | 0.339119 | ||||||||
\(970\) | −7.06295e13 | −2.56161 | ||||||||
\(971\) | 1.65621e13 | 0.597900 | 0.298950 | − | 0.954269i | \(-0.403364\pi\) | ||||
0.298950 | + | 0.954269i | \(0.403364\pi\) | |||||||
\(972\) | 3.73117e12 | 0.134075 | ||||||||
\(973\) | −9.39806e12 | −0.336148 | ||||||||
\(974\) | −1.67357e13 | −0.595840 | ||||||||
\(975\) | −9.27448e12 | −0.328677 | ||||||||
\(976\) | 4.60101e13 | 1.62304 | ||||||||
\(977\) | −3.57670e12 | −0.125591 | −0.0627953 | − | 0.998026i | \(-0.520002\pi\) | ||||
−0.0627953 | + | 0.998026i | \(0.520002\pi\) | |||||||
\(978\) | 2.27120e13 | 0.793837 | ||||||||
\(979\) | −1.50427e11 | −0.00523362 | ||||||||
\(980\) | 4.67955e13 | 1.62064 | ||||||||
\(981\) | 1.09739e13 | 0.378313 | ||||||||
\(982\) | −7.49102e13 | −2.57063 | ||||||||
\(983\) | −3.08375e13 | −1.05339 | −0.526695 | − | 0.850054i | \(-0.676569\pi\) | ||||
−0.526695 | + | 0.850054i | \(0.676569\pi\) | |||||||
\(984\) | 3.48375e13 | 1.18459 | ||||||||
\(985\) | 5.38628e13 | 1.82316 | ||||||||
\(986\) | −1.86586e14 | −6.28684 | ||||||||
\(987\) | 1.66941e13 | 0.559934 | ||||||||
\(988\) | 2.06561e13 | 0.689670 | ||||||||
\(989\) | 3.26234e13 | 1.08429 | ||||||||
\(990\) | −2.56930e13 | −0.850074 | ||||||||
\(991\) | 5.24418e12 | 0.172721 | 0.0863607 | − | 0.996264i | \(-0.472476\pi\) | ||||
0.0863607 | + | 0.996264i | \(0.472476\pi\) | |||||||
\(992\) | −1.30428e13 | −0.427630 | ||||||||
\(993\) | −2.40211e13 | −0.784010 | ||||||||
\(994\) | −3.71661e13 | −1.20756 | ||||||||
\(995\) | 4.60676e13 | 1.49002 | ||||||||
\(996\) | 3.45538e13 | 1.11257 | ||||||||
\(997\) | −3.58536e13 | −1.14922 | −0.574611 | − | 0.818427i | \(-0.694847\pi\) | ||||
−0.574611 | + | 0.818427i | \(0.694847\pi\) | |||||||
\(998\) | −1.23986e13 | −0.395627 | ||||||||
\(999\) | 4.45324e12 | 0.141459 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 177.10.a.a.1.21 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.10.a.a.1.21 | ✓ | 21 | 1.1 | even | 1 | trivial |